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Amanda [17]
3 years ago
9

Solving Quadratic Equations by completing the square xz^2 - 3z - 5 =0

Mathematics
1 answer:
Andrei [34K]3 years ago
8 0

Answer:

x=3z+5

/z^2

Step-by-step explanation:

Let's solve for x.

xz^2−3z−5=0

Step 1: Add 5 to both sides.

xz^2−3z−5+5=0+5

xz^2−3z=5

Step 2: Add 3z to both sides.

xz^2−3z+3z=5+3z

xz^2=3z+5

Step 3: Divide both sides by z^2.

xz^2

/z^2

=

3z+5/

z^2

x=

3z+5

/z^2

Answer:

x=3z+5

/z^2

(/ means over )

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Answer:

\huge\boxed{[-5;\ -2)\ \cup\ [3;\ 13)}

Step-by-step explanation:

The following piecewise functions are linear functions. The graph of any of them is a line segment.

We just need to calculate the value of the function at each end specified in the brace.

y=3x-2\ \text{if}\ -1\leq x

Substitute x =-1 and x = 0:

x=-1\\y=3(-1)-2=-3-2=-5\\\\x=0\\y=3(0)-2=0-2=-2

Range of this piece is [-5; -2)

y=2x+3\ \text{if}\ 0\leq x

Substitute x =0and x = 5:

x=0\\y=2(0)+3=0+3=3\\\\x=5\\y=2(5)+3=10+3=13

Range of this piece is [3; 13)

Therefore the range of the following piecewise function is:

[-5;\ -2)\ \cup\ [3;\ 13)

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How do I solve the equation in an interval from 0 to 2π ? 9 cos 2t = 6​
Ivahew [28]

9\cos(2t)=6\implies\cos(2t)=\dfrac23

Using the fact that cos is 2π-periodic, we have

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That is, \cos(\theta+2n\pi)=\cos\theta for any \theta and integer n.

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